$C_2$-cofiniteness of the vertex algebra $V_L^+$ when $L$ is a non-degenerate even lattice

Details $C_2$-cofiniteness of the vertex algebra $V_L^+$ when $L$ is a non-degenerate even lattice $C_2$-cofiniteness of the vertex algebra $V_L^+$ when $L$ is a non-degenerate even lattice

2009-03-13

arxiv.org/abs/0903.2458v1

Mathematics

Quantum Algebra

Scientific paper

It was shown by Abe, Buhl and Dong that the vertex algebra $V_L^+$ and its irreducible weak modules satisfy the $C_2$-cofiniteness condition when $L$ is a positive definite even lattice. In this paper, we extend their results by showing that the vertex algebra $V_L^+$ and its irreducible weak modules are $C_2$-cofinite when $L$ is a negative definite even lattice and when $L$ is a non-degenerate even lattice that is neither negative definite nor positive definite.

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